This may be a dumb question but are the fonts constantly checked/rebuilt or is it a one-off?
If Build Mode is set to Automatic,
FAM will monitor Add-ons (Install, Uninstall, etc.), templates, style properties and other entities that might contain FA references and does trigger rebuilds If necessary.
So Ideally (though that can't be guaranteed as there might be places that are not monitored) it should catch changes automatically.
A cron would also be possible, but I didn't like this idea as it seems a bit waste of resources to constantly check for changes when most of the time there would not be any changes.
Rather than install anything on the server, is transfonter a suitable option (if it's only ever ran once I don't see why it wouldn't be but if it's constantly ran on a cron I can see why we'd want it locally).
Transfonter should be okay in most cases, but it can't be guaranteed that it will always work (afterall it's a webservice and therefore might be unavailable).
Furthermore it has a limit of 5000 characters for unicode ranges - should be enough in most cases but can be problematic if duotone icons are used extensively.
Last but not least: pyftsubset produces smaller files.
If you can I'd strongly recommended to use pyftsubset.